相关论文: A generalized mean field theory of coarse-graining

If the behavior of a system with many degrees of freedom can be captured by a small number of collective variables, then plausibly there is an underlying mean-field theory. We show that simple versions of this idea fail to describe the…

Partial differential equations are central to describing many physical phenomena. In many applications these phenomena are observed through a sensor network, with the aim of inferring their underlying properties. Leveraging from certain…

A theoretical performance analysis of the graph neural network (GNN) is presented. For classification tasks, the neural network approach has the advantage in terms of flexibility that it can be employed in a data-driven manner, whereas…

The emergence of macroscopic variables can be effected through {\it coarse graining}. Despite practical and fundamental benefits conveyed by this partitioning of state space, the apparently subjective nature of the selection of coarse…

Mean field theory for the time evolution of quantum meson fields is studied in terms of the functional Schroedinger picture with a time-dependent Gaussian variational wave functional. We first show that the equations of motion for the…

A statistical theory of the mean field is developed. It is based on the proposition that the mean field can be obtained as an energy average. Moreover, it is assumed that the matrix elements of the residual interaction, obtained after the…

In order to scale standard Gaussian process (GP) regression to large-scale datasets, aggregation models employ factorized training process and then combine predictions from distributed experts. The state-of-the-art aggregation models,…

A generalization of the Heisenberg algebra has been recently constructed. This generalized algebra has a characteristic function which depends on one of its generators. When this function is linear, $qJ_0+s$, it is possible to construct a…

Many biological systems can be described by finite Markov models. A general method for simplifying master equations is presented that is based on merging adjacent states. The approach preserves the steady-state probability distribution and…

Two coarse-grained models which capture some universal characteristics of stripe forming systems are stud- ied. At high temperatures, the structure factors of both models attain their maxima on a circle in reciprocal space, as a consequence…

A principled method to obtain approximate solutions of general constrained integer optimization problems is introduced. The approach is based on the calculation of a mean field probability distribution for the decision variables which is…

This paper considers generalized linear models using rule-based features, also referred to as rule ensembles, for regression and probabilistic classification. Rules facilitate model interpretation while also capturing nonlinear dependences…

Coarse-graining is a molecular modeling technique in which an atomistic system is represented in a simplified fashion that retains the most significant system features that contribute to a target output, while removing the degrees of…

Mean-Field is an efficient way to approximate a posterior distribution in complex graphical models and constitutes the most popular class of Bayesian variational approximation methods. In most applications, the mean field distribution…

Nonlinear response theory, in contrast to linear cases, involves (dynamical) details, and this makes application to many body systems challenging. From the microscopic starting point we obtain an exact response theory for a small number of…

An algebraic technique is presented that does not use results of model theory and makes it possible to construct a general Galois theory of arbitrary nonlinear systems of partial differential equations. The algebraic technique is based on…

The kinetic field theory is developed without assumptions of statistical homogeneity and isotropy. In a solvable toy model with short-ranged interactions, we compare first-order perturbation theory to an iterated mean-field approximation…

The large time and length scales and, not least, the vast number of particles involved in industrial-scale simulations inflate the computational costs of the Discrete Element Method (DEM) excessively. Coarse grain models can help to lower…

Using the probabilistic language of conditional expectations we reformulate the force matching method for coarse-graining of molecular systems as a projection on spaces of coarse observables. A practical outcome of this probabilistic…

There has been recent progress on the problem of inferring the structure of interactions in complex networks when they are in stationary states satisfying detailed balance, but little has been done for non-equilibrium systems. Here we…